Devlin's
Angle

May 2001

Car Talk Woes

A few weeks ago on NPR's popular afternoon program All Things
Considered, Tom Magliozzi, who together with his brother Ray hosts the
even more popular NPR program Car
Talk, suggested that the teaching of algebra, geometry, and calculus
in schools was a waste of time, and that we'd all be better off if pupils
were taught more useful things.
[You can hear the commentary by clicking here.]

Now, along with millions of other listeners who make Car Talk by
far the most popular show on NPR, I am an avid fan of the Magliozzi
brothers. If tomorrow morning my 1995 Buick Park Avenue with 75,000 miles
on the clock developed a strange
BRRR--CLICK--BRRR-CLICK--BRRR-CLICK sound, Tom and Ray, who go by the
nom-de-radio
Click and Clack, would be the first people I
would turn to for help. When it comes to
cars, they know their stuff.

But when it comes to mathematics, well, Tom, I've gotta tell you, you are
so off base, it's scary. So scary, in fact, that when I heard your
comments, I said to myself:
"This is a smart guy -- heavens, he was a
professor at MIT for many years. How come
he thinks teaching mathematics serves no
useful purpose?"

It didn't take me long to find out. Thanks
to the World Wide Web -- an entirely
mathematical invention by the way -- I was
able to replay Tom's words again, and it was
clear what was going on. The real culprit
isn't Tom, it's the way mathematics so often
gets taught in schools.

The event that prompted Tom's remarks was a back-to-school night at his
son's high school. On the board in the math classroom Tom read the
following statement:

Calculus is the set of techniques that allow us to determine the slope at
any point on a curve and the area under that curve."

AGGGHHH. If I didn't know any better, that
would have made me react the same way as
Tom, although I'm not sure that Tom's phrase
"Who gives a rat's patootie?" works as well
in an English accent as it does in a Car
Talk voice.

Having been a mathematician -- not a math
teacher I should add -- for thirty years, I
can think of dozens of things I might have
written on the board to describe
calculus.

For example: Calculus is a set of techniques
that scientists and engineers use to describe accurately the way things
move -- planets, space shuttles, ballistic missiles, electricity, radio
waves, stock market prices, blood, the heart, the muscles of the body, and
so on.

Or, and this one is designed specially for
Tom: calculus is the set of techniques that
enable automobile designers and
manufacturers to design and build a modern
automobile, with all its moving parts.

Or: calculus was the major intellectual
discovery of the seventeenth century that
made possible the scientific revolution and
all of modern science, technology, and
medicine.

Or: calculus is the language physicists use
to understand the universe and the world we
live in.

Or even simply, calculus is one of the
greatest intellectual achievement of
humankind.

But if you take one of our culture's most
impressive and useful inventions, that quite
literally changed the world, and reduce it
to a trivial statement about finding slopes
of curves, as Magliozzi's son's teacher did,
then there's no wonder Tom reacted the way
he did.

So we shouldn't blame Tom. He's simply the
product of the education he received --
although I wonder who he mixed with during
all those years on the faculty at MIT. And
we shouldn't blame the hapless teacher who
started this whole thing. It may well be
that he or she is doing their best, given
their education. Much of the blame lies in
the way universities train future
mathematics teachers.

Mathematics only exists because it is so
useful. No part of the subject should ever
be taught at school level without explaining
why is was invented and what some of its
uses are. Uses that directly affect everyone
in the classroom.

According to Magliozzi, the purpose of
education is, and I quote, to "help us to
understand the world we live in." That, Tom,
is precisely why some of our ancestors
developed mathematics. Without mathematics,
your weekly show would have to be called
Horse Talk and you and your brother
would have to be called Whinnie and Neigh --
except that without mathematics there
wouldn't be any radio to do it on either, so
you'd have to do it by standing in Harvard
Square and yelling as loud as you could.

By the way, I still think Car Talk is
one of the best programs on radio.